A Brooklyn jury convicted a baby-faced thug of murder Wednesday in the fatal shooting of a livery cab passenger — a case that took a bizarre turn when the veteran prosecutor who brought it to trial failed to show up for closing arguments because he was on a booze-fueled bender.

Michael Magnan, 21, pointed a gun at the cab’s driver in the Flatlands section in 2012 but fired into the backseat when the driver punched him and hit the gas – killing the fare, Nikita Grebelsky, 23, of Queens, in front of his terrified sister.

The trial was interrupted last week when assistant district attorney James Leeper failed to show up for court because he had what a source described as a relapse of his alcoholism and had to check into treatment. The trial was halted for a week while prosecutor Melissa Carvajal got up to speed. Leeper has been suspended.

“His DNA is on the gun that was used to kill a 23-year-old man in front of his sister,” Carvajal said in her closing statement Tuesday.